Question

How many arrangements of the letters of the word TAMILNADU can be made if all the vowels
are always together?

Answer 1

Answer:

a,i,a,u

Step-by-step explanation:

i don't think so that any word form

from these vowels

Answer 2

Answer:

The correct answer is 8640.

Step-by-step explanation:

The word TAMILNADU has 5 consonants and 4 vowels( a,a,i,u).

The vowels should be together always and hence we consider these 4 letters as one unit. However, they can rearrange among themselves( 4!).

The number of ways in which the letters can be arranged are: 6! × 4!

6! - As there are 5 consonants and the vowels together are considered to be one unit( so 6 of them can rearrange among themselves).

So the number if ways =( 6!×4!)/2 ( as the letter 'A' has been repeated twice).

The answer is 8640.